GOODYEAR, Ariz. — Benjamin Edwards gripped a plastic yellow bat, tapped home plate twice and socked each offering up the middle. One by one, Wiffle balls piled up in the outfield grass.

A few hundred yards away, his dad polished off a scoreless inning against his former team, the Rangers.

There was a time when such a setup seemed like an implausible fantasy for a couple conditioned to worst-case scenarios. Well, to an outsider, maybe. Not to Jon Edwards and his wife, Katelyn. They kept believing, even after the diagnosis and the doctor’s plea, after the elbow surgery and the hurdle-filled comeback trail.

Edwards’ journey commenced 13 years ago in Johnson City, Tenn., an 18-year-old outfielder ready to breeze through the Cardinals’ minor-league system. Now, he’s a 31-year-old reliever aiming to secure a spot on the Indians’ Opening Day roster, finally positioned to realize a dream that occasionally flickered, but never quite faded to...